Wettability - New Mexico Institute of Mining and...

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Wettability

Wettability can be defined as the ability of a fluid phase to preferentially wet a solid surface in the presence of a second immiscible phase

Microscopic fluid saturation distribution in a water-wet and oil-wet rock

Wettability

(1) water wet; contact angle q < 90

(2) neutral wettability, q = 90

(3) oil wet, q > 90

Fractional wettability – heterogeneous wetting; i.e., portions of the rock are strongly oil wet, whereas other portions are strongly water wet. Occurs due to variation in minerals with different surface chemical properties. Mixed wettability – refers to small pores occupied by water and are water-wet, while larger pores are oil-wet and continuous.

Wettability

The contact angle is a measure of the wettability of the rock-fluid system, and is related to the interfacial energies by Young’s equation,

where:

sos = interfacial energy between oil and solid, dyne/cm;

sws = interfacial energy between water and solid, dyne/cm;

sow = interfacial energy, or interfacial tension, between oil and water, dyne/cm;

q = contact angle at oil-water-solid interface measured through the water phase,

qsss cosowwsos

Wettability

Sessile drop method of measuring contact angles for water-oil systems

Wettability

USBM method of determining wettability for a water wet sample

• Increasing positive values indicate a preference to water wet; i.e., A1 progressively becomes greater than A2.

Negative values of the index indicate an oil-wet preference (A2 > A1)

Wettability

1. Sample is 100% water saturated,

2. Oil displaces water to Swi, (drainage cycle)

3. spontaneous imbibition of brine, Vosp

4. Water displaces oil to Sor, (imbibition cycle)

5. spontaneous imbibition of oil, Vwsp

6. final displacement of water by oil (2nd drainage cycle).

Combined USBM-Amott Wettability Test

Amott Index

+1 Strongly water wet -1 Strongly oil wet

Capillary Pressure

force up = force down

force up = 2pr s cos q

force down = pr2 h Dg

rdownforcerupforcec

airwghr

Capillary Pressure

In reservoirs, capillary pressure is the difference between the nonwetting phase pressure (Pnw) and the wetting-phase pressure (Pw).

Capillary Pressure

Conversion of lab to reservoir conditions

Example: Laboratory s (air-water) = 72 dyne/cm

q(air-water) = 0

Reservoir s (oil-water) = 24 dyne/cm

q (oil-water) = 30

rw = 65 lb /cu ft ro = 53 lb /cu ft.

reslabc

)(289.0

0cos72

30cos24)()( labc

)(*0.12

rescPc

Capillary Pressure

Entry Pressure Drainage/Imbibition

Capillary Pressure

• Entry pressure

• Irreducible water saturation

• Slope of transition zone curve

• Grain size distribution

• Grain and pore size

Permeability effect

Capillary Pressure Measurement

Mercury injection

Fig. 22 Mercury injection equipment

Sample

Mercury

Displacement reading

Pressure

Schematic of mercury injection apparatus

Example mercury-air capillary pressure curves

Schematic of a Ruska diaphragm pressure cell

Porous Diaphragm

Example of capillary pressure curve for a water-wet system

Centrifuge

sample

rotation

produced in

collection tube

Centrifugal force plays role of gravitational force

Increasing rotation speed ---> increasing force

----> increasing Pc

Gives increasing water production ---> Sw

Fig. 23 Centrifuge

measurement

Capillary pressure measurement by centrifuge

Example capillary pressure curves from centrifugal data. Curves 2 and 4 are estimated because they typically cannot be determined by centrifuge

erNxicP

2610096.1)( r

SdicPSiS

SBAicP

Centrifuge

Schematic illustrating the variation of pressure and water saturation as a function of core length.

Hyperbolic least squares fit

Fig. 24 Measuring Capillary Pressure

Equilibrium Air/Hg Centrifuge

Duration 5 weeks 1day 3 days/run

Max Height (m gas/oil) 30/60 7000/14500 80/160

At stress? Yes Yes No

On cuttings? No Yes No

Sample damaged? No Yes Weak only

Unconsolidated Yes Yes Yes?

Equilibrium reached? Yes Yes Nearly

Clay correction No Yes Norequired

Costs Expensive Cheap Medium

Additional Imbibition Imbibition ImbibitionInformation RI Wettability

Comparison

Capillary Pressure

• Importance in defining: – the height of the transition zone

– the initial distribution of reservoir fluids

– the retention of the wetting phase in the reservoir

• Assign based on: – rock types

– flow process

Averaging Capillary Pressure Data

Methods to fit a laboratory measured capillary pressure curve for the purpose to produce a saturation-height function.

1. Averaging curve fit parameters (e.g. a, b, l vs. f)

Of these the lambda-fit normally works best.

It fits the wetting saturation Sw to the

capillary pressure Pc using three fit constants,

a, b and l, according to: Sw = a.Pc-l + b

2. Interpolation within data set

3. Leverett-J

4. Neural networks

5. Regression (linear, non-linear, multi-variate)

calculate J(Sw) for each capillary pressure

point using:

plot J(Sw) versus Sw and draw a smooth curve

through the points,

reswSJ

Leverett J Function

calculate h for each Sw, for any set of k and f;

plot h versus Sw.

Set of capillary pressure curves for the D sands

Resulting J-function curve for the D-sands

J-function relates rock type (f and k) to Pc and normalizes data for application at different locations in a reservoir

Capillary Pressure

saturation-height as a function of rock type

Capillary Pressure

Causes of errors in capillary pressure curves are:

• Alteration of wettability by invasion of drilling mud filtrate

• Biased sampling

• Sample integrity

• Effect of core cleaning on wettability

• Laboratory measurement and appropriate corrections for temperature, stress, and clays

• Averaging

Log vs core water saturation vs height for a Middle East carbonate

Causes of errors in log calculations are:

• tool calibrations and quality control

• Invasion, thin bed and borehole effects

• Application of the correct interpretation model

• Assumptions or validity of m, n, or a

Also, the difference in “scale” will impact the degree of agreement between core-derived and log-derived saturation-height curves.

Capillary Pressure - PSD

The concept is based on analogy with Carmen-Kozeny’s equation. Recall from the Carmen-Kozeny, k=f(porosity, PSD). Capillary pressure, Pc = f(wettability, saturation), where saturation is a function of pore geometry. Thus a Pc – Sw curve relates the pore size penetrated by the non-wetting fluid at a given capillary pressure.

Where l is a lithology factor ~ 0.216

Compare with CK equation,

2cos24.10S

dSk flqs

Purcell Method

kz = 1/l = 4.63

Capillary Pressure

Define a distribution function, D(ri), The area under the curve at a particular radius represents the fraction of the volume with pores larger than the given radius

Pore radius, microns 0

1087.9(8

Burdine Method

Where xi is a dividing factor to account for the complex geometry of porous media.

Procedure to develop Pc curve for centrifuge measurement and estimate k from Pc curve

Step-by-step procedure

1. Measured data: N, rpms and volume of water displaced, Vdis, cc.

2. Calculate average water saturation:

3. Calculate inlet Pc:

in Kpa

*.14507 in psi

4. Assume values of average water saturation

5. Calculate inlet Pc from a hyperbolic regression fit of Pcinlet=f(Save)

6. Calculate the derivative

7. Calculate the inlet water saturation

erNxicP

2610096.1)( r

SBAicP

SdicPSiS

Capillary Pressure

Capillary Pressure 8. Calculate inlet Pc from regression fit of Pcinlet=f(Sinlet)

9. Calculate the derivative

10. Calculate the pore entry radius, ri

6895 Pa = psi

10,000 microns = cm

dyne/cm2 = .1 Pa

11. Calculate the distribution function from inlet properties

Note: derivative is based on displacing fluid

12. Calculate and graph, Sw vs 1/Pc2

13. Develop a regression fit to the data and integrate

14. Calculate permeability from Purcell's method

l = 0.216

ciPirqs cos2

2cos24.10S

dSk flqs

9843.15594. i

9843.211.1 i

inletcdP

Capillary Pressure

15. Calculate permeability using Burdine's method

a. Summation term approximation

b. Numerical - Composite Simpson's rule

)1( ji

airSTerm D

1087.9(8

Wettability - New Mexico Institute of Mining and...

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